Recent Publications
53. P. J. Pelzl and F. W. King, Convergence accelerator approach for the
high-precision evaluation of three-electron correlated integrals, Physical Review E
57, 7268 (1998).
54. F. W. King, D. G. Ballageer, D. J. Larson, P. J. Pelzl, S. A. Nelson,
T. J. Prosa and B. M. Hinaus, Hylleraas-type calculations of the
relativistic corrections for the ground state of the lithium atom,
Physical Review A 58, 3597 (1998).
55. D. M. Feldmann, P. J. Pelzl and F. W. King, Evaluation of some
integrals arising in relativistic corrections for the atomic
three-electron problem, Journal of Mathematical Physics 39, 6262 (1998).
56. F. W. King, High precision calculations for the ground and excited
states of the lithium atom, Advances in Atomic, Molecular, and
Optical Physics, Academic Press, San Diego, 40, 57 (1999).
57. I. Porras, D. M. Feldmann and F. W. King, A nonlinear programming
approach to the ground state of the helium atom based on lower
bounds to the energy, International Journal of Quantum Chemistry 71, 455 (1999).
58. F. W. King, Convergence accelerator approach for the evaluation of some
three-electron integrals containing explicit rij factors,
International Journal of Quantum Chemistry 72, 93 (1999).
59. P. J. Pelzl, G. J. Smethells, and F. W. King, Improvements on the
application of convergence accelerators for the evaluation of
some three-electron atomic integrals, Physical Review E 65, 036707
(11pg.) (2002).
60. F. W. King, G. J. Smethells, G. T. Helleloid, and P. J. Pelzl, Numerical
evaluation of Hilbert transforms for oscillatory functions: A convergence
accelerator approach, Computer Physics Communications 145, 256 (2002).
61. F. W. King, Efficient numerical approach to the evaluation of
Kramers-Kronig transforms, Journal of the Optical Society of America B
19, 2427 (2002).
62. F. W. King, Reply to "Comment on 'Analysis of some integrals
arising in the atomic four-electron problem' " [J. Chem. Phys.
99, 3622 (1993)], Journal of Chemical Physics 120, 3042 (2004).
63. F. W. King, Alternative approach to the derivation of dispersion
relations for optical constants, Journal of Physics A: Mathematical and General 39, 10427 (2006).
64. F. W. King, Numerical evaluation of truncated Kramers-Kronig transforms, Journal of the Optical Society of America B 24, 1589-1595 (2007).
65. F. W. King, High-precision calculations of the hyperfine constants for the low-lying excited 2S states of the lithium atom, Physical Review A 76, 042512 (2007).
66. D. M. Feldmann and F. W. King, Upper bound to the critical binding nuclear charge for a three-electron atomic system,
Journal of Physics B: Atomic, Molecular and Optical Physics 41, 025002 (2008).
67. F. W. King, Operator basis for analytic signal construction, Multidimensional Systems and Signal Processing, 19, 131-137 (2008).
68. F. W. King, One-center Slater-type integrals with explicit correlation factors, in Recent Advances in Computational Chemistry. Molecular Integrals over Slater Orbitals, edited by Telhat Ozdogan and Maria Belen Ruiz, Transworld Research, Kerala, pp. 39-84, 2008.
69. F. W. King, Hilbert Transforms, Volume I, Cambridge University Press, June, 2009.
70. F. W. King, Hilbert Transforms, Volume II, Cambridge University Press, June, 2009.
71. F. W. King, High precision calculations of the hyperfine constants for the low-lying excited 2S states of Be+, Journal of Physical Chemistry A, 113, 4110-4116 (2009).
72. F. W. King, D. Quicker, and J. Langer, Compact wave functions for the beryllium isoelectronic series, Li- to Ne6+: A standard Hylleraas approach, Journal of Chemical Physics, 134, 124114 (2011).
73. I. Porras, C. D. Schuster, and F. W. King, Convergence accelerator approach to the numerical evaluation of Hilbert transforms based on expansions in Hermite functions, IAENG International Journal of Applied Mathematics, 41, 252-259 (2011).
74. F. W. King, High-precision calculations of the hyperfine constants and some selected transition energies for the low-lying 4S levels of the lithium atom, International Journal of Quantum Chemistry, 113, 2534-2539 (2013).
75. F. W. King, On the evaluation of four-electron correlated integrals with a Slater basis: Some simplifications and some closed form examples, Journal of Physics B: Atomic, Molecular and Optical Physics, 47, 025003 (2014).
76. F. W. King, The evaluation of some four-electron correlated integrals with a Slater basis arising in linear and nonlinear r12 theories, Journal of Physics B: Atomic, Molecular and Optical Physics, 49, 105001 (2016).
77. Chong H. Leong, Ignacio Porras, and F. W. King, Analysis of atomic integrals involving explicit correlation factors for the three-electron case. I. Connection to the hypergeometric function 3F2. Journal of Mathematical Chemistry, 54, 1514-1552 (2016).
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Last Updated: May 27, 2016
Maintained by: fking@uwec.edu